The manufacturer claims that your new car gets 31 mpg on the highway. You suspect that the mpg is less for your car. The 57 trips on the highway that you took averaged 28.8 mpg and the standard deviation for these 57 trips was 10.7 mpg. What can be concluded at the αα = 0.01 level of significance?For this study, we should use The null and alternative hypotheses would be: H0:H0: H1:H1: The test statistic = (please show your answer to 3 decimal places.)The p-value = (Please show your answer to 4 decimal places.)The p-value is ααBased on this, we should the null hypothesis.Thus, the final conclusion is that ...The data suggest that the populaton mean is significantly less than 31 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is less than 31.The data suggest that the population mean is not significantly less than 31 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is less than 31.The data suggest that the sample mean is not significantly less than 31 at αα = 0.01, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is less than 28.8.Interpret the p-value in the context of the study.There is a 6.31117955% chance that the population mean mpg for your car on the highway is less than 31. There is a 6.31117955% chance of a Type I error.If the population mean mpg for your car on the highway is 31 and if you take another 57 highway trips, then there would be a 6.31117955% chance that the population mean mpg for your car on the highway would be less than 31.If the population mean mpg for your car on the highway is 31 and if you drive another 57 times, then there would be a 6.31117955% chance that the sample mean for these 57 trips would be less than 28.8.Interpret the level of significance in the context of the study.If the population mean mpg for your car on the highway is 31 and if you take another 57 trips on the highway, then there would be a 1% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is less than 31.If the population population mean mpg for your car on the highway is less than 31 and if you take another 57 trips on the highway, then there would be a 1% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is equal to 31.There is a 1% chance that the population mean mpg for your car on the highway is less than 31.There is a 1% chance that you own an electric powered car, so none of this matters to you anyway.

For the given data Perform t test for single mean

Answered: The manufacturer claims that your new…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The manufacturer claims that your new car gets 31 mpg on the highway. You suspect that the mpg is less for your car. The 57 trips on the highway that you took averaged 28.8 mpg and the standard deviation for these 57 trips was 10.7 mpg. What can be concluded at the αα = 0.01 level of significance?

For this study, we should use
The null and alternative hypotheses would be:

H0:H0:

H1:H1:

The test statistic = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)
The p-value is αα
Based on this, we should the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest that the populaton mean is significantly less than 31 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is less than 31.
- The data suggest that the population mean is not significantly less than 31 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is less than 31.
- The data suggest that the sample mean is not significantly less than 31 at αα = 0.01, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is less than 28.8.
Interpret the p-value in the context of the study.
- There is a 6.31117955% chance that the population mean mpg for your car on the highway is less than 31.
- There is a 6.31117955% chance of a Type I error.
- If the population mean mpg for your car on the highway is 31 and if you take another 57 highway trips, then there would be a 6.31117955% chance that the population mean mpg for your car on the highway would be less than 31.
- If the population mean mpg for your car on the highway is 31 and if you drive another 57 times, then there would be a 6.31117955% chance that the sample mean for these 57 trips would be less than 28.8.
Interpret the level of significance in the context of the study.
- If the population mean mpg for your car on the highway is 31 and if you take another 57 trips on the highway, then there would be a 1% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is less than 31.
- If the population population mean mpg for your car on the highway is less than 31 and if you take another 57 trips on the highway, then there would be a 1% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is equal to 31.
- There is a 1% chance that the population mean mpg for your car on the highway is less than 31.
- There is a 1% chance that you own an electric powered car, so none of this matters to you anyway.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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